How can I train to stop my newest chihuahua not to bark and bite my other one?

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First of all, don't give your dog a lot of attention when he barks. Try to ignore him. When you give him a lot of attention, or yell at him, you are reinforcing the barking. Give him a treat and praise him when he is quiet. You could try putting a leash on him, and whenever he barks, remove him from the room. This will take time and patience. So far as biting the other one, you can praise him and give him a treat every time he comes in contact with and is calm with the other one.

How long have you had the newest one? Bringing a new dog into a home with another dog seldom results in instant friendliness! The new dog is usually nervous and the first dog is feeling left out and abandoned, especially if a new dog is barking and biting him. Give them both some space and some individual attention. Remember, feed the old guy first since he was there first and the new one doesn't know she isn't supposed to get fed first! I would also get into the habit of feeding them in separate rooms or, even better, in their crates.
How old is the new one? If it's a puppy, it is probably somewhat frightened of the other one so the less you acknowledge it's barking, the better it is...give them some time to get used to each other.